Question

The average annual salary of the employees of a company in the year 2005 was ninety thousand dollars. It increased by the same factor each year and in 2006, the average annual salary was $91,200. Let f(x) represent the average annual salary, in thousand dollars, after x years since 2005. Which of the following best represents the relationship between x and f(x)?

f(x) = 91.2(1.013)x
f(x) = 90(1.013)x
f(x) = 91.2(2.2)x
f(x) = 90(2.2)x

Answer 1

Increasing Factor: 91200/90000 = 1.013

Each year, after 2005, the salary is the previous salary times 1.013

Then in 2006, when x = 1, salary = 90 * (1.013)
In 2007, when x = 2, salary = 90*(1.013)*(1.013) = 90(1.013)^2

After x years, salary = 90(1.013)^x

Answer 2

Given:
Year 0 = 2005 = 90,000
Year 1 = 2006 = 91,200

(91,200 - 90,000)/90,000 = 1,200/90,000 = 0.013

f(x) = 90(1.013)x
f(1) = 90(1.013)1
f(1) = 91.170

The second option, f(x) = 90(1.013)x, is the best representation of the relationship between x and f(x).